I purchased a 1903 rifle that looks like the NRA sporter rifle. But I can not be sure and I need help identifying this gun. It is a military rifle all the way. It is marked Rock Island Armory on the receiver and the serial number is 326XXX. It has the Lyman 48 receiver sight and there are cartouches on the stock ("SA" on the buttstock and a "P" in a circle behind the trigger guard. The Barrel is marked with a bomb with fire coming out of it just behind the front sight. Can anybody help me ID this gun?

One quick way is the forward band.  If the band molds around the barrel, then it has the appearance of an NRA sporter.  Most of the "sporterized" rifles either did away with the front band or used the oval original band and kept part of the upper hand guard.